The Generalized Discrimination Score for Ensemble Forecasts

This article refers to the study of Mason and Weigel, where the generalized discrimination score D has been introduced. This score quantifies whether a set of observed outcomes can be correctly discriminated by the corresponding forecasts (i.e., it is a measure of the skill attribute of discrimination). Because of its generic definition, D can be adapted to essentially all relevant verification contexts, ranging from simple yes no forecasts of binary outcomes to probabilistic forecasts of continuous variables. For most of these cases, Mason and Weigel have derived expressions for D, many of which have turned out to be equivalent to scores that are already known under different names. However, no guidance was provided on how to calculate D for ensemble forecasts. This gap is aggravated by the fact that there are currently very few measures of forecast quality that could be directly applied to ensemble forecasts without requiring that probabilities be derived from the ensemble members prior to verification. This study seeks to close this gap. A definition is proposed of how ensemble forecasts can be ranked; the ranks of the ensemble forecasts can then be used as a basis for attempting to discriminate between corresponding observations. Given this definition, formulations of D are derived that are directly applicable to ensemble forecasts.